# An object with a mass of 4 kg is acted on by two forces. The first is F_1= < -2 N , 4 N> and the second is F_2 = < 3 N, -8 N>. What is the object's rate and direction of acceleration?

Jul 24, 2017

The rate of acceleration is $= 1.12 m {s}^{-} 2$ in the direction is $= {116.6}^{\circ}$ anticlockwise from the x-axis.

#### Explanation:

The resultant force is

$\vec{F} = {\vec{F}}_{1} + {\vec{F}}_{2}$

$= < - 1 , 4 > + < 3 , - 8 >$

$= < 2 , - 4 >$

The acceleration is

$\vec{a} = \frac{1}{4} \cdot < 2 , - 4 > = < \frac{1}{2} , - 1 >$

The rate of acceleration is

$= | | < \frac{1}{2} , - 1 > | | = \sqrt{\frac{1}{4} + 1} = \frac{\sqrt{5}}{2} = 1.12 m {s}^{-} 1$

The direction is $\theta = \arctan \left(- \frac{1}{\frac{1}{2}}\right) = \arctan \left(- 2\right) = {116.6}^{\circ}$ anticlockwise from the x-axis